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04 May 2021, 22:25
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MathRevolution
Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.
Now we will solve this DS question using the Variable Approach.
Let’s apply the 3 steps suggested previously.
Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.
We have to find whether ‘n’ is an even integer.
Follow the second and the third step: From the original condition, we have 1 variable (n). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.
Recall 3- Principles and Choose D as the most likely answer. Let’s look at each condition separately.
Condition (1) tells us that n – 5 is an even integer.
=> n – 5 = even.
=> n = even + 5 = odd - YES
The answer is unique YES, so the condition (1) alone is sufficient, according to CMT 1 - there must be a unique YES or a NO.
Condition (2) tells us that \(\frac{n}{5}\) is an odd integer.
=> \(\frac{n}{5}\) = odd.
=> n = 5 * odd = odd - YES
The answer is unique YES, so condition (2) alone is sufficient, according to CMT 1 - there must be a unique YES or a NO.
Each condition alone is sufficient.
Therefore, D is the correct answer.
Answer: D
04 May 2021, 22:33
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Que: If x is an integer, is \(x^2 - x\) a multiple of 18?
(1) x- 1 is an even integer.
(2) x is an odd integer.
(1) x- 1 is an even integer.
(2) x is an odd integer.
05 May 2021, 22:18
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Bookmarks
MathRevolution
Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.
Now we will solve this DS question using the Variable Approach.
Let’s apply the 3 steps suggested previously.
Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.
We have to find ‘Is \(x^2 - x\) a multiple of 18’- where ‘x’ is an integer
Modify the question:
=> \(x^2 – x = 18p?\) – where ‘p’ is an integer
=> x(x-1) = 18p?
So, we have to find whether x or x-1 is a multiple of 18?
Condition (1) tells us that x - 1 is an even integer
=> x – 1 = even.
=> x = even + 1 = odd
=> If x = 3 or 9 , it is multiple of 18 - YES
=> But if x = 5 or 7 , it is not multiple of 18 - NO
The answer is not unique, so the condition (1) alone is not sufficient, according to CMT 1 - there must be a unique YES or a NO.
Condition (2) tells us that x is an odd integer
=> If x = 3 or 9 , it is multiple of 18 - YES
=> But if x = 5 or 7 , it is not multiple of 18 - NO
The answer is not unique, so condition (2) alone is not sufficient, according to CMT 1 - there must be a unique YES or a NO.
Combining both the conditions (1) and (2), we get x is odd
=> If x = 3 or 9 , it is multiple of 18 - YES
=> But if x = 5 or 7 , it is not multiple of 18 - NO
The answer is not unique, so the conditions combined are not sufficient, according to CMT 1 - there must be a unique YES or a NO.
Conditions combined are not sufficient.
Therefore, E is the correct answer.
Answer: E
